System and method for providing scanning polarized reference sources

ABSTRACT

A method of providing a polarized radio frequency scanning source is provided. The method including amplitude modulating at least two synchronized polarized radio frequency (RF) carrier signals with a predetermined relationship between their amplitude modulation of their electric field components and their polarization states to provide a scanning polarized RF reference source with a desired scanning range, pattern and frequency. The two or more synchronized polarized RF carrier signals with the predetermined relationship between their amplitude modulation can obtain a periodic or non-periodic scanning range, rate and frequency.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application is a continuation application of U.S.application Ser. No. 11/888,797 filed Aug. 2, 2007 which claims priorityto U.S. provisional patent application, Ser. No. 60/835,022, filed onAug. 2, 2006, the entire contents of each of which is incorporatedherein by reference.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates generally to scanning sources and, moreparticularly, to systems and methods for providing scanning polarizedreference sources.

2. Prior Art

For guidance and/or steering purposes, all manned and unmanned mobileplatforms, such as land vehicles, powered or non-powered airborneplatforms, surface or submerged marine platforms, or various spacevehicles, require onboard information as to their absolute (relative toearth) position and orientation (sometimes called attitude) or theirposition and orientation relative to another object such as a referenceplatform or a target object.

This position and orientation information is particularly important forunmanned and guided platforms such as mobile robots. Unmanned AerialVehicles (UAV), unmanned guided surface or submerged platforms, and thelike. This is also the case in future smart and guided projectiles,including gun-fired munitions, mortars and missiles. Such platforms willalso require the aforementioned absolute and/or relative position andorientation information onboard the platform for closing the feedbackguidance and control loop to guide the platform to the desired target ortrack a specified trajectory or the like.

In certain cases, the onboard position and orientation information(absolute or relative to the target, a reference station, another mobileplatform, etc.) can be provided by an outside source, for example, byGPS for position or by a radar reading or optical signal that isreflected off some target or received by the mobile platform. In othercases, it is either required or is highly desirable to have autonomoussensors on board the mobile platform, including gun-fired projectiles,mortars and missiles, to directly measure the position and orientationof the object with respect to a fixed object (for example a groundstation) or a moving object (for example a moving target).

It is noted that even though in this disclosure all references are madeto moving platforms, it will be appreciated by those of ordinary skillin the art that the provided description also includes the measurementof the position and orientation of one object relative to anotherobject, one or both of which may be fixed to a third object such as theground.

Currently available sensors for remote measurement of the angularposition (attitude) of an object relative to the earth or another object(target or weapon platform) can be divided into the following five majorclasses.

The first class of sensors measure changes in the angular position usinginertial devices such as accelerometers and gyros. Inertial basedangular orientation sensors, however, generally suffer from drift andnoise error accumulation problems. In such sensors, the drift and themeasurement errors are accumulated over time since the acceleration hasto be integrated twice to determine the angular position. As a result,the error in the angular position measurement increases over time. Inaddition, the initial angular orientation and angular velocity of theobject must be known accurately. Another shortcoming of inertia basedangular position sensors is that the angular position of one objectrelative to another cannot be measured directly, i.e., the orientationof each object relative to the inertia frame has to be measuredseparately and used to determine their relative angular orientation. Asa result, errors in both measurements are included in the relativeangular orientation measurement, thereby increasing it even further. Inaddition, electrical energy has to be spent during the entire time tocontinuously make such sensory information.

In the particular case of gun-fired munitions, two other major problemsare encountered with inertia-based sensors. Firstly, they have to bemade to withstand firing accelerations that in certain cases could be inexcess of 100,000 Gs. However, to achieve the required guidance andcontrol accuracy over relatively long distances and related times, theabsolute angular orientation of the projectile has to be known duringthe entire time of the flight within very small angles corresponding tosub-fractions of one G. As a result, the accelerometer is prone to asettling time problem, particularly with the aforementioned initial highG loading. Obviously, the development of inertia based accelerometersand gyros that could withstand the aforementioned high G levels andrequire near zero settling time is an extremely difficult task.

The second class of angular orientation sensors operates using opticalmethods. Such sensory systems can directly measure angular position ofone object relative to another. However, optical based angular positionsensory systems suffer from several disadvantages, including operationonly in the line of sight between the two objects; accurate measurementof relative angular orientation only if the objects are relatively closeto each other; limited range of angular orientation measurement;relatively high power requirement for operation; requirement ofrelatively clean environment to operate; and in military applicationsthe possibility of exposing the site to the enemy and jamming. Opticalgyros do not have most of the above shortcomings but are relativelylarge, require a considerable amount of power, and are difficult toharden for high G firing accelerations. Optical methods such as trackingof projectiles with surface mounted reflectors and the like have alsobeen developed, which are extremely cumbersome to use even duringverification testing, suffer from all the aforementioned shortcomings,and are impractical for fielded munitions. In addition, the informationabout the object orientation can usually be determined only at theground station and has to be transmitted to the moving object forguidance and control purposes. As a result, optical angular positionsensors are generally not suitable for munitions and other similarapplications.

The third class of angular orientation sensors is magnetometers that canbe used to measure orientation relative to the magnetic field of theearth. The main problem with magnetometers is that they cannot measureorientation of the object about the magnetic field of the earth. Otherimportant issues are low sensitivity; requirement of an accurate map ofthe magnetic field in the area of operation; and sensitivity to thepresence of vehicles and the like in the area, the configuration ofwhich usually varies in time, particularly in an active war theatre.

The fourth class of angular orientation measurement systems are based onthe use of radio frequency (RF) antennas printed or placed on thesurface of an object to reflect RF energy emanating from a ground-basedradar system. The reflected energy is then used to track the object onthe way to its destination. With two moving objects, the radar measuresthe time difference between the return signals from each of the objectsand thereby determines angular information in terms of the angle thatthe relative velocity vector makes with respect to a coordinate systemfixed to one of the objects. With such systems, measurement of fullspatial orientation of an object (relative to the fixed radar or asecond object) is very difficult. In addition, the information about theobject orientation is determined at the radar station and has to betransmitted back to the moving object(s) if it is to be used for coursecorrection. It is also very difficult and costly to develop systems thatcould track multiple projectiles. It is noted that numerous variationsof the above method and devices have been devised with all sufferingfrom similar shortcomings.

In addition to the above angular orientation measurement sensors. GPSsignals have also been used to provide angular orientation information.Such systems, however, have a number of significant shortcomings,particularly for munitions applications in general and gun firedmunitions and mortars in particular. These include the fact that GPSsignals may not be available along the full path of the flight; suchorientation sensory systems are generally not very accurate; and themeasurements cannot be made fast enough to make them suitable forguidance and control purposes in gun fired munitions and mortars. Inaddition, GPS signals are generally weak and prone to jamming.

The fifth class of angular orientation sensors is based on utilizingpolarized Radio Frequency (RF) reference sources and mechanical cavitiesas described in U.S. Pat. Nos. 6,724,341 and 7,193,556 and U.S. patentapplication publication number 2007/0001051, all of which areincorporated herein by reference, and hereinafter are referred to as“polarized RF angular orientation sensors”. These angular orientationsensors use highly directional mechanical cavities that are verysensitive to the orientation of the sensor relative to the referencesource due to the cross-polarization and due to the geometry of thecavity. The reference source may be fixed on the ground or may beanother mobile platform (object). Being based on RF carrier signals, thesensors provide a longer range of operation. The sensors can also workin and out of line of sight. In addition, the sensors make angularorientation measurements directly and would therefore not accumulatemeasurement error. The sensor waveguides receive and record theelectromagnetic energy emitted by one or more polarized RF sources. Theangular position of a waveguide relative to the reference source isindicated by the energy level that it receives. A system equipped withmultiple such waveguides can then be used to form a full spatialorientation sensor. In addition, by providing more than one referencesource, full spatial position of the munitions can also be measuredonboard the munitions.

The aforementioned polarized RF based angular orientation sensorsprovide highly precise angular orientation measurements. The sensors,when embedded in a mobile platform such as in a projectile, can measurefull angular orientation of the projectile (mobile platform) relative tothe fixed ground station or another moving object such as a UAV oranother projectile (mobile platform) where the reference source islocated. These angular orientation sensors are autonomous, i.e., they donot acquire sensory information through communication with a ground,airborne or the like source. The sensors are relatively small and can bereadily embedded into the structure of most mobile platforms includingmunitions without affecting their structural integrity. As a result,such sensors are inherently shock, vibration and high G accelerationhardened. A considerable volume is thereby saved for use for other gearand added payload. In addition, the sensors become capable ofwithstanding environmental conditions such as moisture, water, heat andthe like, even the harsh environment experienced by munitions duringfiring. In addition, the sensors require a minimal amount of onboardpower to operate.

The latter two classes of RF based full angular orientation and fullposition sensors promise to provide low cost, small volume andlightweight, low power, precision and autonomous onboard sensors forguidance and control of all mobile platforms, including future smart andprecision guided munitions, as alternatives to inertia-based, optical,GPS and other similar currently available sensors.

The latter two classes of RF based full angular orientation sensors aredependent on the magnitude of the received signal at the sensors fromthe reference source to determine the orientation of the sensor relativeto the reference source. This is the case, for example, for theaforementioned angular orientation sensors which are based on utilizingpolarized Radio Frequency (RF) reference sources and mechanical cavitiesas described in U.S. Pat. Nos. 6,724,341 and 7,193,556 and U.S. patentapplication publication number 2007/0001051.

Briefly, referring now to FIGS. 1 and 2, there is shown a representationof a waveguide sensor 100 and its operation with respect to a polarizedradio frequency (RF) reference (illuminating) source 101. Anelectromagnetic wave consists of orthogonal electric (E) and magnetic(H) fields. The electric field E and the magnetic field H of theilluminating beam are mutually orthogonal to the direction ofpropagation of the illumination beam. When polarized, the planes of Eand H fields are fixed and stay unchanged in the direction ofpropagation. Thus, the illuminating source establishes a (reference)coordinate system with known and fixed orientation. The waveguide 100reacts in a predictable manner to a polarized illumination beam. Whenthree or more waveguides are distributed over the body of an object, andwhen the object is positioned at a known distance from the illuminatingsource, the amplitudes of the signals received by the waveguide sensor100 can be used to determine the orientation of the object relative tothe reference (illuminating) source 101, i.e., in the aforementionedreference coordinate system of the reference source 101. The requirementfor the proper distribution of the waveguide sensors 100 over the bodyof the object is that at least three of the waveguides be neitherparallel nor co-planar.

It is therefore observed that the aforementioned classes of RF basedfull angular orientation sensors are dependent on the magnitude of thereceived signal at the sensors from the reference source to determinethe orientation of the sensor relative to the reference source. The useof the signal magnitude, however, has several major shortcomings thatlimits the utility of such sensors as well as degrades their angularorientation measurement precision. The following are the majorshortcomings of the aforementioned use of signal magnitude informationin these sensors for measuring angular orientation relative to thepolarized RF reference source:

-   -   1. To relate the magnitude of the received signal to angular        orientation, the distance from the reference source to the        angular orientation sensors must be known. This in general means        that other means have to be also provided to measure or indicate        the position of the orientation sensor relative to the reference        source.    -   2. In practice, the signal received at the angular orientation        sensor would be noisy, it may face losses due to the        environmental conditions, and is also prone to measurement        errors at the sensor.    -   3. The magnitude of the signal received at the angular        orientation sensors and its relationship to the angular        orientation of the sensors (object to which the sensors are        attached) could be significantly different when the object is        not in the line-of-sight of the reference source. Therefore when        the object is not in the line-of-sight, the use of the received        signal magnitude information could in general lease to        significant degradation of the accuracy of the angular        orientation measurements.

SUMMARY OF THE INVENTION

The use of polarized RF reference sources with scanning capability wouldsignificantly reduce or eliminate the aforementioned shortcomings of theRF based full angular orientation sensors. This would be the case sincescanning provides the means to use various well established techniquessuch as peak detection and a novel nonlinear signal processing methodbased on a curve matching and scaling, which is disclosed later in thisdisclosure, and thereby significantly increase the angular orientationmeasurement precision, in certain cases by several orders of magnitude;filtering out the noise and effects of reflections and multi-paths;making it possible to use these angular orientation sensors in bothline-of-sight and non-line-of-sight settings; and also eliminates theneed to know the distance between the reference source and the angularorientation sensors. It is also shown later in this disclosure that theuse of polarized RF reference sources with scanning capability wouldhave additional advantages. For example, the precision with which theangular orientation is measured by the sensors is not dependent on theaccurate calibration of the received signal magnitude information(usually surfaces). In addition, particularly for line-of-sightapplications, if such calibration has been made, then as discussedbelow, the information can be used to calculate the distance between thereference source to the sensors (object) as well.

In addition, when more than one polarized RF reference source is used tomeasure the position of the sensors (object) in the coordinate systemfixed to the reference sources, the use of polarized RF referencesources with scanning capability would significantly increase theaccuracy of these measurements.

A need therefore exists for polarized RF reference sources with scanningcapability. This is particularly the case since such reference sourceswould allow the aforementioned RF angular orientation sensors to be usedin both line-of-sight as well as in non-line-of-sight, in addition tomaking them significantly more accurate and tolerant to noise and otherenvironmental effects, and when calibrated would allow them to measuredistance between the reference source and the angular orientationsensors (object) in addition to the angular orientation measurement.

An objective of the present invention is to provide a method and systemfor polarized RF reference sources with scanning capability, therebyallowing a significant increase in the angular orientation measurementprecision of the aforementioned angular orientation sensors; filteringout the noise and effects of reflections and multi-paths; making itpossible to use these angular orientation sensors in both line-of-sightand non-line-of-sight settings; and measure the distance between thereference source and the angular orientation sensors (object),particularly in line-of-sight situations. Such polarized RF referencesources with scanning capability can be designed to provide almost anydesired scanning range and scanning frequency, ranging from Hz to KHz oreven MHz frequencies, even non-sinusoidal patterns, to fit theapplication at hand.

Another objective of the present invention is to provide a novelnonlinear signal processing method based on a curve matching and scalingtechnique, thereby increasing the accuracy of the angular orientation(and distance between the reference source and the sensors, i.e.,object, particularly in line-of-sight situations) measurement of theaforementioned angular orientation sensors. In certain applications, theuse of non-sinusoidal scanning patterns has added advantages, some ofwhich are described below.

Another objective of the present invention is to provide a method andsystem for establishing an angular orientation reference source for alarge area, for example the field of operation of certain mobileplatforms, such as the field of operation of mobile robotic platformsbeing used for rescue operations in certain fields. Such a referencingsystem may be used to serve as a full positioning as well angularorientation system.

Yet another objective of the present invention is to provide the methodand system of establishing “homing” planes and/or lines (with or withoutdirectional indication) and/or points. Such “homing” “signals” can thenbe used by the mobile platform for guidance, e.g., for guiding ittowards or away from a point or move towards a line and then followcertain.

It is noted that the disclosed methods and systems can allow thescanning capability of the present polarized RF source to be achievedwithout the use of any mechanical components and by the use of simpleelectronic circuitry using modulated signals of various patterns. As aresult, the scanner can achieve almost any rate, any scanning pattern,scanning frequencies ranging from zero to several Hz, or KHz, or MHzdepending on the application at hand.

In addition, the disclosed polarized RF reference sources with scanningcapability can be programmed to provide random scanning signals withvery low power levels or on-off (pulsed) signals to avoid detection orutilize other detection avoidance procedures.

In addition, the disclosed method can readily allow the prior artpolarized RF reference sources to scan more than one range, for examplefor providing a relatively narrow scanning range for more than oneangular orientation.

BRIEF DESCRIPTION OF THE DRAWINGS

These and other features, aspects, and advantages of the apparatus ofthe present invention will become better understood with regard to thefollowing description, appended claims, and accompanying drawings where:

FIGS. 1 and 2 illustrate a schematic representation of a waveguidesensor with respect to a polarized radio frequency (RF) reference(illuminating) source of the prior art.

FIG. 3 illustrates a graph where m_(x)=0, m_(y)=0.5, and E_(0x)=E_(0y),and the reference sources are positioned at the origin of the CartesianXY coordinate system O.

FIG. 4 illustrates a scanning polarized RF reference source positionedat the origin of the Cartesian XYZ coordinate system.

FIG. 5 illustrates two scanning polarized RF reference sources withcorresponding mean directions of polarization lines.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

An electromagnetic wave is a propagation of electric and magnetic fielddisturbances in unison such that both electric and magnetic fieldvectors are perpendicular to the direction of propagation and to eachother, they are in phase and in vacuum the ratio of their magnitude isconstant. The wave is transverse (oscillations are perpendicular to thedirection of propagation) and its velocity in free space is determinedby the permittivity and permeability of free space. The polarizationstate of an electromagnetic wave is defined by the oscillation state ofits transverse electric field in the plane perpendicular to propagationdirection. Since the magnetic field is always perpendicular to theelectric field and has a proportional magnitude it is redundant for thecharacterization of polarization. The magnitudes and phases oforthogonal components of electric field do not necessarily have the samevalues and the periodic curve traced out by the tip of the electricfield vector describes the different states of polarization.

The electromagnetic waves in free space are described by the Maxwellequations without the charges and currents are

  ∇E = ?   ∇B = 0$\mspace{20mu} {{\nabla E} = \frac{\text{?}B}{\text{?}}}$$\mspace{20mu} {{\nabla B} = {\text{?}\frac{\text{?}B}{\text{?}}}}$?indicates text missing or illegible when filed

where E and B are respectively the electric and magnetic (induction)fields, and ε₀ and μ₀ respectively denote the permittivity andpermeability of free space. From Maxwell's equations one derives thefollowing linear wave equations

$\mspace{20mu} {{\text{?}\frac{\text{?}E}{\text{?}}} = {\nabla^{2}E}}$$\mspace{20mu} {{\text{?}\frac{\text{?}B}{\text{?}}} = {\nabla^{2}B}}$?indicates text missing or illegible when filed

which implies that

c=1/√{square root over (ε₉μ₀)}

the wave (phase) speed c.

To specify the polarization state of electromagnetic waves we look forthe harmonic traveling plane wave solutions of the electric field waveequation describing the waves propagating in the z-direction. Inorthogonal coordinates XYZ these solutions are given by

E(z,t)=E i+E _(y) j-E _(0x) cos(ω−kz)+E _(0x) cos(ω−kz−δ)j

where ω is the angular frequency, δ denotes the phase angle differencebetween the x and y components of electric field. k is the z-componentof wave number vector which is related to the wavelength λ with |k−2π/λand parallel to the direction of propagation. E_(0x) and E_(0y) are the(positive) amplitudes of x and y components of electric fieldcomponents, respectively, and i and j are unit vectors in the x and ydirections of the aforementioned Cartesian coordinate system XYZ.

Consider a situation in which the polarization states associated withthe components E_(x) and E_(y) are given as

E _(x) =E _(0x) cos(ωt−kz)

E _(y) =E _(0y) cos(ωt−kz+δ)

Then the following characteristic can be defined:

-   a) For δ : 2 πn, n 1, 2, 3, . . . , the electric field components    are in phase and their ratio E_(x) E_(y) is a positive constant, in    this case we have a so-called linearly polarized or plane polarized    wave. The tip of electric field vector traces out a line in the    xy-plane which defines the polarization direction, and

E _(x) =E _(0x) cos(ωt−kz)

E _(y) =E _(0y) cos(ωt−kz)

-   b) For δ −π: 2 π n, n 1, 2, 3, . . . , we have an out of phase    linear polarization with the component ratio equal to a negative    constant, and

E _(x) =E _(0x) cos(ωt−kz)

E _(y) =−E _(0y) cos(ωt−kz)

-   c) For δ π 2 : 2 π n, n 1, 2, 3, . . . , and E_(0x) E_(0y), the    electric field vector rotates in the xy-plane clockwise (as seen    against propagation) without changing its magnitude and it is in a    state of right circular polarization, and

E _(x) =E _(0x) cos(ωt−kz)

E _(y) =−E _(0y) sin(ωt−kz)

-   d) For δ −π2 : 2 π n, n 1, 2, 3, . . . , and E_(x0) E_(0y), the    electric field rotates counterclockwise; this specifies a left    circular polarization, and

E _(x) =E ₀ cos(ωt−kz)

E _(y) =E ₀ sin(ωt−kz)

-   e) For δ -π 2=2 π n, n -1, 2, 3, . . . and E_(x0)≠E_(0y), we have a    more general case of right elliptical polarization. Electric field    components have different amplitudes and the y-component leads with    ninety degrees of phase; the tip electric field vector rotates    clockwise and traces out an ellipse, and

E _(x) =E _(0x) cos(ωt−kz)

E _(y) =−E _(0y) sin(ωt−kz)

f) For δ −π 2−2 π n, n −1, 2, 3, . . . and E_(x0)≠E_(0y), the electricfield rotates counterclockwise and its tip again traces out an ellipse;this is a state of left elliptical polarization.

In the general case

E _(x) =E _(0x) cos(ωt−kz)

E _(y) =E _(0y) cos(ωt−kz+δ)

where the magnitudes of electric field components E_(0x) and E_(0y) arenot necessarily equal and value of the phase difference δ is arbitrary,one can derive the curve traced out by the tip of electric field vectorin the xy-plane (which is the plane of electric field components). Byeliminating the phase (ωt kz) we obtain

$\mspace{20mu} {{( \frac{\;_{\text{?}}}{E_{0_{x}}} )^{2} + ( \frac{\;_{\text{?}}}{\;_{\;_{\text{?}}}\text{?}} )^{2} - {2( \frac{\;_{\text{?}}}{E_{0_{x}}} )( \frac{\;_{\text{?}}}{\text{?}} )\cos \; \delta}} = {\sin^{2}\delta}}$?indicates text missing or illegible when filed

which specifies a tilted ellipse in E_(x) and E_(y) coordinates. Theazimuth angle ψ (0≦ψ≦π 2) between the x-axis and the major semi-axis ofthis ellipse then becomes

${\tan \; 2\psi} = {( \frac{2\; E_{0_{x}}E_{0_{y}}}{E_{0_{x}}^{2} - E_{0_{y}}^{2}} )\cos \; \delta}$

The following relations are also valid between the amplitudes of theelectric field components and the lengths a and b of semi-major andsemi-minor axes which specify the ellipticity of the polarizationellipse:

a² ·b² E_(0x) ² |E_(0y) ²   1.

2. a b 2. E_(0x) ² E_(0y) ² sin δ  2.

where the signs specify the sense of electric field rotation.

tan 2 104 tan α cos δ  3.

where tan α−E_(0x)/E_(0y) and 0≦α≦π/2

sin 2 φ−-tan α sin δ  4.

with tan γφ=(b/a), where -(π/4)≦φ≦)π/4).For the phase difference δ=0 and δ=π, the ellipse degenerates to

$\mspace{20mu} {\text{?}_{\text{?}} = {{\pm ( \frac{E_{0_{y}}}{E_{0_{x}}} )}\text{?}}}$?indicates text missing or illegible when filed

which is the equation of a straight line, and it specifies a linearpolarization. For δ=:π/2 and E_(0x) -E_(0y)=E₀, the ellipticalpolarization curve reduces to a circle, which defines a circularpolarization

E _(x) ² +E _(y) ² =E ₀ ²

The novel methods disclosed herein utilize amplitude modulation of atleast two synchronized polarized Radio Frequency (RF) carrier signalswith an appropriate relationship between their amplitude modulation oftheir electric field components and their polarization states to providea scanning polarized RF reference source with the desired scanningrange, pattern and frequency. The polarized RF carrier signals arepreferably in GHz range to yield relatively small scanning polarized RFreference sources.

As it is noted above, at least two synchronized polarized RadioFrequency (RF) carrier signals with appropriate relationship betweentheir amplitude modulation are required to construct the disclosedpolarized RF reference sources with scanning capability. In thefollowing formulations and for the sake of making the formulationssimple, the present novel method of providing scanning polarized RFreference sources is described for two synchronized polarized RadioFrequency (RF) carrier signals E₁ and E₂, where both are linearlypolarized, one with only a component in the x and one with only acomponent in the y direction of the aforementioned Cartesian coordinatesystem XYZ, as

E ₁ =E _(x) cos(ω−kz)i

E ₂ =E _(y) cos(ω−kz |δ)j

where ω is the angular frequency, δ denotes the phase angle differencebetween the two electric fields, x and y components of electric field, kis the z-component of wave number vector. It is sufficient toconcentrate on the behavior of this field in the z−0 plane to sec theeffects of amplitude modulation. Formally amplitude modulation isrepresented by replacing the amplitudes E_(x) and E_(y) of the aboveelectric fields by functions of time as

E _(x) =A _(x)(t)cos(ωt)

E _(y) =A _(y)(t)cos(ωt+δ)

where the modulation amplitudes A_(x) and A_(y) may be any functions,but preferably a superposition of many harmonic functions correspondingto a range of modulation frequencies and they can represent variouswaveforms. In general, the variations of modulation amplitudes aredesired to be significantly slower relative to the fast oscillations ofthe carrier waves. i.e., they are almost ‘constant’ on a time durationof the order of one period of these fast oscillations.

A relatively simple amplitude modulation of the above polarized carrierwaves may be selected as

E _(x) =E _(0x)(1+m _(x) sin Ωt)cos ωt

E _(y) =E _(0y)(1+m _(y) sin Ωi)cos(ωtδ)

where Ω is the angular modulation frequency (in our case, the scanningfrequency of the desired scanning polarized RF reference source), whichis much smaller than ω and the constants m_(x) and m_(y) denote themodulation indices of x and y components. These indices are generallysmaller than unity to avoid ‘over-modulation’. Specifically we may, forexample, choose a left elliptical polarization (counterclockwiserotation) by setting δ=−π/2 and write

E _(x) =E _(0x)(1+m _(x) sin Ωt)cos ωt

E _(y) =E _(0y)(1+m _(y) sin Ωt)sin ωt

These components are not periodic functions of a single common frequencyand the curve defined by the electric field vector is not ‘closed’;however a particular value of the modulation frequency Ω can be chosento satisfy these conditions. Let us impose the condition that there is acommon period T between the modulation and carrier signals. Theperiodicity condition for the x-component

E _(x) =E _(0x)[1+m _(x) sin Ω(t+T)] cos ω(t+T)=E _(0x)(1+m _(x) sinΩt)cos ωt

is satisfied if

$\Omega = {\frac{n}{m}\omega}$

for some integers n and m. Thus if the ratio of modulation and carrierfrequencies is a rational number then one can choose a single period forthe x-component (same is also true for the y-component). In addition, tohave a periodic (closed) curve traced out by the tip of electric fieldvector there must be a common period between the field components. Thecomponents E_(x) and E_(y) can also be written as

$E_{x} = {{E_{0_{x}}\cos \; \omega \; t} + {\frac{E_{0_{x}}m_{x}}{2}{\sin \lbrack {( {\omega + \Omega} )t} \rbrack}} - {\frac{E_{0_{x}}m_{x}}{2}{\sin \lbrack {( {\omega - \Omega} )t} \rbrack}}}$$E_{y} = {{E_{0_{y}}\sin \; \omega \; t} + {\frac{E_{0_{y}}m_{y}}{2}{\cos \lbrack {( {\omega - \Omega} )t} \rbrack}} - {\frac{E_{0_{y}}m_{y}}{2}{\cos \lbrack {( {\omega + \Omega} )t} \rbrack}}}$

which reveal the sideband frequencies ω−Ω and ω+Ω. The ellipse equationspecified by the tip of modulated electric field (for δ=−π/2) transformsto

$\mspace{20mu} {{{\frac{1}{M_{x}^{2}}( \frac{E_{x}}{E_{0_{x}}} )^{2}} + {\frac{1}{M_{y}^{2}}( \frac{\;_{\text{?}}}{\text{?}} )^{2}}} = 1}$?indicates text missing or illegible when filed

where we set

M_(x)≡(1+m_(x) sin Ωt)

M_(y)≡(1+m_(y) sin Ωt)

This represents a ‘modulated ellipse’ whose semi-major and semi-minor‘axes’ change their lengths periodically and relatively slowly with afrequency Ω. If the magnitudes of the electric field components areequal, say to E₀, the circular polarization is modulated to anelliptical one with periodically changing axial lengths as described by

${( \frac{E_{x}}{E_{0}M_{x}} )^{2} + ( \frac{E_{y}}{E_{0}M_{y}} )^{2}} = 1$

One embodiment is the general case or linear polarization in which theslope of polarization plane is replaced by a periodic function.

$\begin{matrix}{\mspace{79mu} {{\text{?} = {{\pm \frac{E_{0_{\text{?}}}}{E_{0_{x}}}}( \frac{1 + {m_{y}\sin \; \Omega \; t}}{1 + {m_{x}\sin \; \Omega \; t}} )E_{x}}}{\text{?}\text{indicates text missing or illegible when filed}}}} & (1)\end{matrix}$

Thus if the modulation indices of the two components of the electricfields E_(0x) and E_(0y) are equal (i.e., if m_(y) m_(x)), then theslope of polarization line remains the same. This isobviously not ofinterest since the polarization line is not varied over a certain range.i.e., the resulting polarized RF reference source does not have ascanning feature.

However, if for example, only the y-component is modulated. i.e., ifm_(x)=0, and an in-phase polarization is considered, the slope ofpolarization line is replaced by a simple periodically changing functiongiven in equation (2), and the polarization line would vary over acertain range depending on the values of the parameters m_(y), E_(0x),and E_(0y), and the resulting polarized RF reference would thereforebecome a scanning polarized RF reference source:

$\begin{matrix}{\mspace{79mu} {{\text{?} = {\frac{E_{0_{y}}}{E_{0_{x}}}( {1 + {m_{y}\sin \; \Omega \; t}} )E_{x}}}{\text{?}\text{indicates text missing or illegible when filed}}}} & (2)\end{matrix}$

which is the ‘trace’ of curve

E_(x)=E_(0x) cos ωt

E _(y) =E _(0x)(1+m _(y) sin Ωt)cos Ωt

True trace, set of points (E_(x), E_(y)) lying on the curve, is obtainedby entirely eliminating the time variable

$\begin{matrix}{\mspace{79mu} {{\text{?} = {\frac{E_{0_{y}}}{\text{?}}\{ {1 + {\text{?}{\sin \lbrack {( \frac{\Omega}{\omega} )\text{?}( \frac{E_{x}}{\text{?}} )} \rbrack}}} \} E_{x}}}{\text{?}\text{indicates text missing or illegible when filed}}}} & (4)\end{matrix}$

For Ω<<ω sin function can be approximated by its argument, reducing thecurve to

$\begin{matrix}{\mspace{79mu} {{\text{?} = {{\frac{\text{?}}{\text{?}}\lbrack {1 + {\text{?}( \frac{\Omega}{\omega} )\text{?}( \frac{E_{x}}{E_{0_{x}}} )}} \rbrack}E_{x}}}{\text{?}\text{indicates text missing or illegible when filed}}}} & (5)\end{matrix}$

The equation (1) represents one of the simplest (harmonic) classes ofamplitude modulation for the present novel scanning polarized RFreference sources constructed with two synchronized polarized RadioFrequency (RF) carrier signals with appropriate relationship betweentheir amplitude modulation. It will however, be appreciated by those ofordinary skill in the art that an infinite number of such classes ofperiodic and even non-periodic functions may be formed with two or moresynchronized polarized Radio Frequency (RF) carrier signals withappropriate relationship between their amplitude modulation to obtainvarieties of preferably periodic and even non-periodic scanning ranges,rates and “scanning pattern” (hereinafter, the time history of thepolarization line is referred to as the “scanning pattern”).

In addition, even though the above two superimposed linearly polarizedplane waves were in orthogonal directions, the only requirement toachieve the desired scanning range and pattern is that the two (or more)waves not be collinear. In fact, for relatively small scanning ranges,the E vector of the two linearly polarized plane waves may be desired tobe less than 90 degrees apart to minimize the required scanner power forthe same power levels at the receiving sensor position.

It is noted that the selection of an appropriate scanning pattern isdependent on the application at hand, for example for the polarized RFangular orientation measurement sensors previously described, and thealgorithms used to extract the desired information, for example peakdetection and/or pattern matching for angular orientation measurement.

In one embodiment, the classes of amplitude modulation represented byequation is used to construct scanning polarized RF reference sourceswith two synchronized polarized Radio Frequency (RF) carrier signals aspreviously described. One of the simplest versions of this class ofamplitude modulation may be obtained by setting the component m_(x) 0,thereby obtaining a “scanning pattern” that consists of a simpleharmonic motion, equation (2). For the simple harmonic scanning patterngiven by equation (2), the parameters consisting of the constantmagnitudes of the two components of the electric fields E_(0x) andE_(0y) and the constant modulation index of the y component m_(y)determine the mean direction of the polarization line and the range ofthe scanning angle.

For example, consider the case of m_(x)=0, m_(y)=0.5, and E_(0x)−E_(0y),and considering that the reference sources are positioned at the originof the Cartesian XY coordinate system O, FIG. 3. Then the polarizationline 10 is readily shown to scan from the angle β₁=26.6 deg. (obtainedby setting Sin Ω t=−1 in equation (2) to obtain the slope of thepolarization line. i.e., β₁=tan⁻¹(E_(y)/E_(x))=tan⁻¹(0.5)=26.6 deg.),also indicated as numeral 12 in FIG. 3, to β2=56.3 deg. (obtained bysetting Sin Ω t=1 in equation (2) to obtain the slope of thepolarization line, i.e., β₂=tan⁻¹(E_(y)/E_(x))−tan⁻¹(1.5)=56.3 deg.),also indicated as numeral 13 in FIG. 3, for a total range of thescanning angle of about γ=29.7 degrees, also indicated as numeral 11 inFIG. 3.

As can be seen in FIG. 3, with the selected parameters for the scanningpattern described by equation (2), a range of about 29.7 degrees 11 canbe scanned. In a similar manner, by choosing different values for theconstant parameters m_(x), m_(y), E_(0x), and E_(0y), different meandirection and scanning ranges are obtained with the scanning patterndescribed by the equation (1).

In general, any desired scanning pattern may be implemented with theproposed method. For example, one may choose scanning patterns withpeaks that are sharper than a simple harmonic sine wave, therebyincreasing the accuracy of a peak detection algorithm. Alternatively,one may add specially designed patterns that will simplify a patterndetection algorithm being used and/or to reject noise, and/or to reducetheir susceptibility to detection and jamming, or for other applicationspecific purposes.

It is noted that the following method may also be used to provide two oreven more simultaneous and arbitrarily oriented scanning referencesources. Such multi-range scanning is useful for the establishment of anetwork of reference sources and/or to limit the range or radiation whenmultiple sensors (for example, munitions and/or weapon platforms) areusing the reference source.

It is noted that the linearly polarized and synchronized Radio Frequency(RF) carrier signals used to construct the disclosed scanning polarizedRF reference sources (for example, the two linearly polarized planewaves E_(y) and E_(x) of equation (2) that were superimposed in theabove formulations) may be generated using almost any of the methods anddevices that arc commonly used in the art, including by using apertureantennas. It is also noted that in many applications, such as in theguidance and control of most mobile platforms, the angular orientationand/or position information may not need to be known as a continuousfunction of time and information may be required (for example forguidance and control purposes) only at discrete and sometimes even atinfrequent points of time. In such applications, the scanning polarizedRF reference source needs to provide its signal only when theaforementioned angular orientation and/or position information is neededonboard the mobile platform.

In another embodiment, at least two scanning polarized RF referencesources may be used so that the aforementioned polarized RF basedangular orientation sensors, for example mounted on a mobile platform,could determine the position and/or orientation of the sensors, i.e.,the mobile platform, relative to the scanning polarized RF referencesources.

Now consider the situation in which a scanning polarized RF referencesource 20 is positioned at the origin O of the Cartesian XYZ coordinatesystem as shown in FIG. 4. The scanning polarized RF reference source 20is considered to have a scanning range 21, with the mean direction ofthe polarization line (for example, with a simple harmonic patternpreviously described) indicated by the vector 22. Now let an object(e.g., a mobile platform) 23 with an embedded aforementioned polarizedRF angular orientation sensor 24 that is properly designed to receivethe carrier frequency signal to be positioned as shown in FIG. 4. Usingwell known peak detection techniques, the direction 26 of a linepassing, through the polarized RF angular orientation sensor 24 andparallel with the direction of the mean direction of the polarizationline, i.e., the vector 22 is determined.

It is noted that if the line 26 coincides with the mean direction of thepolarization line 22, then the signal received at the polarized RFangular orientation sensor 24 is maximum and the distance 25 between thelines 26 and 22 is zero. For example, if the scanning pattern of thescanning polarized RF reference source 20 is a simple harmonic patternas previously described, then the peak of the received signal is reachedwhen the mean direction of the polarization line 22 intersects thepolarized RF angular orientation sensor 24 and signal received by thesensor 24 is also substantially a simple harmonic signal (neglecting anynoise and other commonly present sources of distortion). However, if thedistance 25 between the lines 26 and 22 is not zero, then the signalreceived by the sensor 24 is distorted with the peak leaning to one sideor the other depending on whether the line 26 is placed below the meandirection of the polarization line 22 (as shown in FIG. 4) or on itsopposite side.

The amount of above peak distortion would therefore serve as a sensoryinformation indicating the direction that the mobile platform 23 has totravel (perpendicular to the line 26) in order to reduce the distance25, and would also provide the information onboard the mobile platform23 indicating when it is positioned along the mean direction of thepolarization line 22. It can therefore be said that the polarized RFangular orientation sensor 24 that is attached to the mobile platform 23can use the signal from the scanning polarized RF reference source 20 to“home-in” and align itself to the mean direction of the polarizationline 22.

It is noted that if the distance between the scanning polarized RFreference source 20 and the line 26 is known, then for an arbitrarypositioning of the mobile platform 23, the distance 25 between the lines22 and 26 can in general be determined from the magnitude of thereceived signal.

Now consider the situation in which two (or more) scanning polarized RFreference sources 30 and 31 with corresponding mean directions of thepolarization lines 32 and 33, respectively, are used as shown in FIG. 5.Let also a mobile platform 34 with at least one polarized RF angularorientation sensor 35 be positioned somewhere a distance away but in thescanning range of the two scanning polarized RF reference sources 30 and31 as shown in FIG. 5. Using the method described above, the pattern ofthe signal received at the polarized RF angular orientation sensor 35from each one of the two scanning polarized RF reference sources 30 and31, the polarized RF angular orientation sensor 35 would provide sensoryinformation to the mobile platform 34 for guidance (homing-in) towardsthe mean direction of the polarization lines 32 and 33, i.e., towardsthe point of their intersection 36. The only requirement for this modeof operation of the scanning polarized RF reference sources is that thetwo mean directions of the polarization lines 32 and 33 are notparallel.

It is noted that the polarization lines 32 and 33 are in fact theintersections of planes of polarization with the XY plane (FIG. 4). Theaforementioned point of intersection 36 (FIG. 5) is also a lineperpendicular to the above XY plane and directed parallel to the Z axisof the Cartesian XYZ coordinate system (FIG. 4).

It is noted that by varying the direction of the polarization line 32and 33 (FIG. 5), the point of their intersection 36 towards which themobile platform 34 is guided can be changed in a dynamic mode.

It is also noted that by using at least three scanning polarized RFreference sources that are properly oriented, a mobile platform may bedirected to any position in space.

In general, by using more scanning polarized RF reference sources thanare necessary, the positioning precision of the above methods isincreased.

Although the scanning source has been described in terms of RF energy,other types of energy can also be used, such as x-rays.

While there has been shown and described what is considered to bepreferred embodiments of the invention, it will, of course, beunderstood that various modifications and changes in form or detailcould readily be made without departing from the spirit of theinvention. It is therefore intended that the invention be not limited tothe exact forms described and illustrated, but should be constructed tocover all modifications that may fall within the scope of the appendedclaims.

1. A method of providing a polarized radio frequency scanning source,the method comprising amplitude modulating at least two synchronizedpolarized radio frequency (RF) carrier signals with a predeterminedrelationship between their amplitude modulation of their electric fieldcomponents and their polarization states to provide a scanning polarizedRF reference source with a predetermined scanning range, pattern andfrequency.
 2. The method of claim 1, wherein the two or moresynchronized polarized RF carrier signals with the predeterminedrelationship between their amplitude modulation obtain a periodicscanning range, rate and frequency.
 3. The method of claim 1, whereinthe two or more synchronized polarized RF carrier signals with thepredetermined relationship between their amplitude modulation obtain anon-periodic scanning range, rate and frequency.
 4. A polarized radiofrequency scanning source comprising means for amplitude modulating atleast two synchronized polarized radio frequency (RF) carrier signalswith a predetermined relationship between their amplitude modulation oftheir electric field components and their polarization states to providea scanning polarized RF reference source with a predetermined scanningrange, pattern and frequency.